ARTICLE pubs.acs.org/JPCC
TDDFT Study of the Optical Absorption Spectra of Bare and Coated Au55 and Au69 Clusters R. W. Burgess and V. J. Keast* School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia ABSTRACT: The optical absorption of bare and ligand-coated Au55 and Au69 “Schmid” clusters was calculated using timedependent density functional theory. Calculations were performed using the explicit time propagation method with the local density approximation for the exchange-correlation potential. Both icosahedral and cuboctahedral structures of the Au55 gold core were simulated. The ligand coating was shown to have the effect of reducing the features of the optical absorption spectrum of the clusters, giving a profile more similar to experimental results. The difference in the optical absorption between the different geometries and core sizes is also less marked when the clusters are coated. The results suggest that within the 1.4 nm size range, the absorption spectra are dominated by the coating and are not experimentally distinguishable. Binding energies were also calculated for the Au55 cluster, showing that the cuboctahedral structure has lower energy although the energy difference is very small. The effect of the coating on the electron density of the gold cluster is also investigated by subtracting the electron densities of the bare clusters from those of the coated clusters.
’ INTRODUCTION Metal nanoparticles are currently of great technological interest due to their unique optical properties.1,2 They can show high nonlinearity, tunable absorption, and the potential for the manipulation of light using structures smaller than one wavelength.3 5 Gold particles can be fabricated to bridge the middleground between individual atoms and bulk materials in a continuous fashion.6,7 In small clusters quantum effects become apparent and a classical description of the properties is no longer accurate.2,8 Ligand passivated gold particles are of particular interest because of their stability and that they can be produced in monodisperse solutions.9,10 Several such solutions have been synthesized, including Au102(SR)44,10,11 Au25(SR)18,12 Au38(RS)2,413,14 and Au144(RS),15 among others. One cluster that has attracted significant interest is the Au55(PPh3)12Cl6 “Schmid” cluster.16,17 A number of experimental studies have been dedicated to the Schmid structure, including optical absorption,18 21 XPS,22 24 conductivity,25 and M€ossbauer spectroscopy measurements.26 Measurements of the optical absorption of the Schmid cluster showed a featureless absorption spectra with decreasing absorption cross-section for increasing wavelength.18 20 Another measurement on films of the Schmid cluster showed a peak attributed to plasmon absorption at 2.4 eV, as well as another distinct peak at 6.0 eV.21 Also measured was an absorption peak at around 1 eV. This peak disappeared after further heating, leading to the hypothesis that this peak was caused by ellipsoidal particles in the sample.21 Initial specification of the stoichiometry was based on preference for a 55 atoms cluster, and supported by M€ossbauer spectroscopy measurements.27 A cluster of 55 atoms was preferred r 2011 American Chemical Society
because a 55 atom cluster corresponds to a full shell cluster. A full shell cluster comprises of a single atom, surrounded by complete shells of atoms, ending in a perfect external geometry, and can have either icosahedral or cuboctahedral geometries. The number of atoms in each subsequent shell is given by 10n2 + 2 where n is the shell number. This gives cluster sizes of 13, 55, 147, 309, etc. The stability of clusters containing these numbers of atoms was first observed for Xenon using yields in a mass spectrometer.28Ligand-coated clusters of transmission metals including gold were synthesized having numbers of metal atoms corresponding to full shell clusters 17 and coated clusters with Pt30929 and Pd205730 cores have been observed under high resolution transmission electron microscopy (HRTEM), further supporting full-shell clusters of transmission metals. However, there is also evidence that the cluster may have a different stoichiometry, and it has been proposed that a freeelectron shell closing picture is a better predictor of cluster stability.31 33 Most recently the results from density functional theory (DFT) have been used to claim that this cluster is better represented as Au69(Ph3)20Cl12.34 It should be noted that the computational work performed so far has neglected kinetic and entropic effects and uses the approximation of replacing the phenyl groups by H. The experimental evidence for the size and stoichiometry is inconclusive and sometimes contradictory.35 40 Images obtained in the transmission electron microscope17,20 suggest that, although the size distribution is narrow, there is a Received: July 25, 2011 Revised: September 25, 2011 Published: September 27, 2011 21016
dx.doi.org/10.1021/jp207070n | J. Phys. Chem. C 2011, 115, 21016–21021
The Journal of Physical Chemistry C
ARTICLE
Bare gold clusters of sizes 1 14 atoms46 48 and 20 atoms48 51 have had their optical absorption spectra calculated by TDDFT. Smaller ligand-coated gold particles have also had their optical absorption calculated, including Au25(RS)188,52 and Au38(RS)24.53,54 Bare clusters of other metals have also been analyzed using TDDFT, including silver,55 sodium,56 58 and lithium.57,59 Clusters with up to 120 silver atoms have had their optical absorption calculated with TDDFT.60 To our knowledge, no TDDFT calculations have been reported for either the Au55 cluster or the recently suggested alternative Au 69 cluster, either coated or bare. Theoretical calculations of the optical properties could help resolve between competing atomic structures, and improved understanding of the optical properties of these larger gold clusters would assist in fabricating clusters with desirable optical properties for technological applications.42 This work investigated the optical response of bare and coated Au55 and Au69 clusters and the effect of the ligand coating to the optical response of the gold cluster. The connections between charged bare Au55 clusters and coated clusters is explored, and the calculated optical response is compared to experimental measurements in the literature.18 21
Figure 1. Structures simulated in this work. The left-hand column shows the bare clusters, while the right-hand column shows the coated clusters. Starting from the top, the icosahedral Au55, cuboctahedral Au55, and Au69 clusters. Gold atoms are yellow, the phosphorus atoms are orange, the hydrogen atoms are shown as white, and the chlorine atoms are green.
significant range of particle sizes. The experimental work suggests that more than one stoichiometry for the particles occurs and the material preparation methods may play a role. Despite the uncertainty about the stoichiometry for the Au55(PPh3)12Cl6 cluster, there has been significant research to determine its structure. HRTEM images of coated Pt30929 and Pd205730 cores indicated a cuboctahedral geometry to the central core. This gave early preference to cuboctahderal arrangements for full shell transmission metal clusters, including Au55. Symmetry considerations of Au55(PPh3)12Cl6 further support the cuboctahedral structure: a cuboctahedron has 12 vertices and 6 square faces, matching the 12 phosphine groups and 6 Cl atoms of Au55(PPh3)12Cl6.17,18 This is contradicted by investigations of the bare cluster using density functional theory (DFT), which suggest a distorted icosahedron to be the lowest energy structure.7,41 Given the large number of atoms and the large volume involved, DFT simulations of the full coated cluster have not yet been performed. Instead an intermediate Au55(PH3)12Cl6 cluster was investigated, which again showed a distorted icosahedral geometry to have the lowest energy.42,43 These calculations resulted in a structure with a central atom surrounded by an icosahedron of 12 gold atoms 0.29 nm from the center and a second icosahedron of 12 atoms at 0.58 nm. The remaining 30 gold atoms are arranged roughly on the edges of the outer icosahedron but at a distance of 0.51 nm from the central atom. The PH3 groups are bonded to the vertices of the outer icosahedron and the chlorine atoms arranged on 6 of the 20 faces (see Figure 1). Time-dependent DFT (TDDFT) can be viewed as an extension of traditional DFT to the time-dependent domain, allowing calculation of properties such as optical absorption spectra.44,45
’ COMPUTATIONAL DETAILS All calculations were performed using the TDDFT package Octopus.45 Within Octopus calculations are performed over a discrete grid in real-space and ground state electron distributions are calculated under DFT. The time propagations for TDDFT are performed over discrete steps in real-time. The real-space grid used was contained in a volume consisting of a series of overlapping spheres of radius 3.5 Å with a sphere centered on each atom. The spacing between grid points within this volume was 0.2 Å. Testing on smaller gold particles showed that this gave good convergence of the total energy and electron density. Fully relativistic pseudopotentials were generated under the improved Troullier and Martins method61 using the Ceperly and Alder LDA exchange-correlation potential.62 Ground state calculations were performed using a Fermi-Dirac type electron smearing to simulate an electronic temperature and to ease convergence of open-shell systems.63 In all cases a smearing of 0.01 eV was used. Six structures were studied; two bare Au55 clusters, two Au55(PH3)12Cl6 clusters, a bare Au69 cluster and a Au69(PR3)20Cl12 cluster (see Figure 1). A bare cuboctahedral structure was cleaved directly from a bulk crystal, a coated icosahedral and bare icosahedral structure were generated following the arrangement of Periyasamy and Remacle.42 The coated cuboctahedral structure was generated by placing a PH3 group bonded onto each of the 12 gold atoms located on a vertex and a chlorine atom bonded onto the 6 gold atoms centered in the middle of each square face. Finally, the Au69(PR3)20Cl12 used is the same as used in the work of Walter et al.,34 and the bare Au69 is the same cluster but with the coating removed. The bare Au55 structures were relaxed, and then coatings were added to the relaxed bare structure. Relaxation of the coated cluster allowing movement of the gold atoms resulted in negligible movement (
